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A193981
Number of ways to arrange 3 nonattacking triangular rooks on an nXnXn triangular grid
2
0, 0, 0, 2, 23, 127, 468, 1352, 3310, 7190, 14260, 26330, 45885, 76237, 121688, 187712, 281148, 410412, 585720, 819330, 1125795, 1522235, 2028620, 2668072, 3467178, 4456322, 5670028, 7147322, 8932105, 11073545, 13626480, 16651840, 20217080
OFFSET
1,4
COMMENTS
Column 3 of A193986
LINKS
Christopher R. H. Hanusa, Thomas Zaslavsky, A q-queens problem. VII. Combinatorial types of nonattacking chess riders, arXiv:1906.08981 [math.CO], 2019.
FORMULA
Empirical: a(n) = 6*a(n-1) -14*a(n-2) +14*a(n-3) -14*a(n-5) +14*a(n-6) -6*a(n-7) +a(n-8)
Contribution from Vaclav Kotesovec, Aug 31 2012: (Start)
Empirical: G.f.: -x^4*(2 + 11*x + 17*x^2)/((-1+x)^7*(1+x))
Empirical: a(n) = 13*n/24 - 11*n^2/24 - 23*n^3/48 + 9*n^4/16 - 3*n^5/16 + n^6/48 + 1/4*floor(n/2)
(End)
EXAMPLE
Some solutions for 5X5X5
......0..........0..........0..........0..........0..........0..........0
.....0.0........0.0........0.0........0.0........0.1........0.0........0.1
....0.0.1......1.0.0......0.1.0......0.1.0......0.0.0......0.1.0......1.0.0
...0.1.0.0....0.0.0.1....1.0.0.0....0.0.0.1....1.0.0.0....1.0.0.0....0.0.0.0
..1.0.0.0.0..0.1.0.0.0..0.0.1.0.0..0.0.1.0.0..0.0.1.0.0..0.0.0.0.1..0.0.0.1.0
CROSSREFS
Sequence in context: A041579 A185830 A301665 * A235594 A053299 A356828
KEYWORD
nonn
AUTHOR
R. H. Hardin Aug 10 2011
STATUS
approved